The factorial of a number, n!, is defined for whole numbers as the product of all integers from 1 to n.

For example, 5! is 5 * 4 * 3 * 2 * 1 = 120

Most factorial implementations use a recursive function to determine the value of factorial(n). However, this blows up the stack for large values of n - most systems cannot handle stack depths much greater than 2000 levels.

Write an implementation to calculate the factorial of arbitrarily large numbers, without recursion.

Rules

• n < 0 should return nil/ None
• n = 0 should return 1
• n > 0 should return n!

Note

Codewars limits the amount of data it will send back and forth, which may introduce a false ceiling for how high of a value of n it will accept. All tests use values less than this limit.